Intermodulation is the production of spurious signals having frequencies corresponding to the sum and difference frequencies of the fundamentals and their harmonics produced by a nonlinear element, such as a diode or amplifier. For applications including, but not limited to, multi-user cellular satellite communications systems, the nonlinearity is typically created by High Power Amplifiers (HPAs) driven into saturation. However, these amplifiers operate more efficiently when they are driven near saturation. Thus, the system designer strives to optimize the performance of the HPAs by selecting an optimal operating point for all the HPAs based on the particular application.
For practical systems, the intermodulation (IM) power generated by the HPAs is dominated by third-order effects having sum and difference terms which are difficult to filter and therefore lead to nonlinear distortion. This distortion diverts a portion of the input power to various harmonics. As such, it is desirable to minimize the effect of IM power on the received signals. The signal to IM power ratio may be used to measure this effect. This ratio may be improved by either increasing the signal power or decreasing the IM power. However, an increase in signal power may actually result in more significant IM distortion depending upon the operating point of the corresponding amplifier(s). Reduction of IM power for a particular signal or beam may be accomplished by spatial dispersion of the IM power across multiple beams or cells. As such, it is useful to quantify the spatial dispersion of IM power which is the improvement in signal to IM power ratio from the HPAs on a satellite to the received signals on the ground.
Standard simulation techniques quantify IM power by generating time domain samples of the input waveform to each HPA, then using an HPA transfer characteristic to compute time domain samples of the output waveform from the HPA. This widely accepted simulation technique has a running time proportional to the product of the total number of time samples considered and the total number of HPAs in the simulation. For multi-user cellular systems, this technique requires long running times because the number of HPAs in such a system is typically large, and because such multi-user signals are typically wide-band, which requires a large number of samples in the simulation. For practical systems with several hundred users and over 100 HPAs, the standard simulation technique is prohibitively slow and thus not feasible.